Static and Kinematic Indeterminacy Farmula: Easy way to External and Internal indeterminacy.

In Structural Analysis, Indeterminacy is a concept that tells you whether you can solve a structure using only the basic equations of equilibrium

and

∑M = 0

As a Civil Engineer, you’ll find that mastering these formulas is the fastest way to score marks in exams and design safe structures.

1. Static Indeterminacy (Ds)

Static Indeterminacy occurs when the number of unknown forces (reactions and internal forces) is greater than the available equilibrium equations.

External Indeterminacy (Dse)

This relates to the supports of the structure.

• Formula:

  Dse = R - r

  • R = Number of support reactions.

  • r = Number of equilibrium equations (usually 3 for 2D structures, 6 for 3D).

Internal Indeterminacy (Dsi)

This relates to the geometry of the structure (members and joints).

• For Beams: Always 0 (unless there is a closed loop).

• For 2D Trusses:

  Dsi = m - (2j - 3)

• For 2D Frames:

  Dsi = 3 x (Number of closed loops)

Total Static Indeterminacy:

Ds = Dse + Dsi

2. Kinematic Indeterminacy (Dk)

Kinematic Indeterminacy (also called Degrees of Freedom) refers to the number of independent joint displacements (translations and rotations) possible in a structure.

The Easy Way to Calculate Dk (2D Structures):

• For 2D Frames:

  Dk = 3j - R

• For 2D Trusses:

  Dk = 2j - R

  • j = Number of joints.

  • R = Number of support reactions.

Note: If the members are considered inextensible (length doesn't change), subtract the number of members (m) from the result.

• Revised Formula:

  Dk = (3j - R) - m